Logical Reasoning

PT155 · S1 · Q15 Most cats like to go outside

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Most cats like to go outside to play when the temperature is above freezing.

Information

quantifier (most)

Most cats = like to go out and play when temp > freezing

conditional (unless = if not)

If there is not cat not allowed at least one → to go out member outside

conditional (only when = right side)

family members → sun is shining go outside or hot outside

Evaluate

Whenever we see a conditional idea in an Inference stimulus, we make it the center of our attention look for two possible moves: 1. can we chain it up with other conditionals (if any)? 2. can we apply it to any provided facts (may have to contrapose)?

Since we noticed two conditional indicators, "unless" and "only when", we should start by figuring out whether they chain together. We may have to contrapose our conditionals to see where they would line up. They need some overlapping claim, and in this case the overlapping idea is whether or not Jamil's family members are outside.

The easiest way to chain stuff together mentally is to use "X requires Y" language. Any conditional, X → Y, can be read as "X requires Y".

In order for the cat to be allowed outside, there must be a family member outside. And in order for there to be a family member outside, it has to be sunning or hot (or both).

We can write that chain of requirements, if we think it will help us maintain a clear image of the chain.

Cat some family sun's shining allowed → members → or outside are outside hot outside

What about the first sentence, the Most claim? Can we apply this rule to that sentence? Are there any overlapping ideas?

Not really. The concept of "likes to go outside and play" is not the same as "whether the cat is allowed to go outside". And the concept of "when the temperature is above freezing" isn't a good match for ideas like "Sun's shining / hot outside".

The temperature could be above freezing whether or not the sun is shining, and whether or not it's hot outside.

We could say that . But it would be pretty awkward to add that on to the chain, because it would build off the "hot outside" half of our Or outcome.

It's probably more likely that the first sentence just isn't intended to combine with the 2nd and 3rd claims.

Goal

Look for an answer rewarding us for having assembled that chain of requirements, but pick any answer we can prove from the provided information.

15.

Which one of the following can be properly inferred from the information above?

If Jamil's cat is outside,
Bad Trigger / Outcome Match
We don't have any knowledge triggered by "If J's cat is outside". We know that "If J's cat is allowed outside, then some family members are out there, which means it's sunny, hot, or both." Cat some family sun's shining allowed → members → or outside are outside hot outside But the cat might be outside without being allowed outside. And even if we played along and equated those, we just know that it's sunny, hot, or both. We can't prove that the temperature is above freezing. The sun can be shining, even when the temperature is freezing or colder.
5% picked this
If Jamil's cat is not
Illegal Negation
We don't have any knowledge triggered by "If J's cat is not outside". We know that "If J's cat is allowed outside, then some family members are out there, which means it's sunny, hot, or both." Cat some family sun's shining allowed → members → or outside are outside hot outside This answer is trying to flip the lightswitch on all these ideas, which is illegal. It's thinking, Cat not no family sun's not shine allowed → members → or outside are outside not hot outside
3% picked this
If the sun is shining
Illegal Reversal
We don't have any knowledge triggered by "If sun is shining or hot outside". That's an outcome, not a trigger. Cat some family sun's shining allowed → members → or outside are outside hot outside This answer is trying to read backwards, which is illegal. It's thinking, Cat some family sun's shining allowed ← members ← or outside are outside hot outside
7% picked this
If at least one member
Illegal Reversal
We do have some knowledge triggered by "If some family members are outside". That tells us that it's sunny, hot, or both. Cat some family sun's shining allowed → members → or outside are outside hot outside This answer is trying to read backwards, which is illegal. It's thinking, Cat some family sun's shining allowed ← members ← or outside are outside hot outside
6% picked this
Correct
If the sun is not
Why this is right
This provides the contrapositive of the chain we derived. Cat some family sun's shining allowed → members → or outside are outside hot outside When we contrapose A → B → C or D we get ~D and ~C → ~B → ~A So the contrapositive of our chain is ~sun shining no fam cat not and → members → allowed ~hot outside outside outside That's what this answer is reflecting, "If this 1st thing, then this 3rd thing". The answer does add on an assumption that "if the cat is not allowed outside, then the cat is not outside". That is definitely not something we were told, and it's not a common sense truth that "whenever cats aren't allowed outside, they are not outside", because we all know cats escape sometimes. So this serves as a nice reminder that the "best" answer on a must be true might not literally be 100% derivable, but it will always be the most supportable option.
Skill tested: Must be True · how this choice captures the argument's function is the move to repeat next time.
78% picked this

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